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<div class="title">IncompleteCholesky.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2012 Désiré Nuentsa-Wakam &lt;desire.nuentsa_wakam@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2015 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_INCOMPLETE_CHOlESKY_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_INCOMPLETE_CHOlESKY_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &lt;list&gt;</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> UpLo_ = Lower, <span class="keyword">typename</span> OrderingType_ = AMDOrdering&lt;<span class="keywordtype">int</span>&gt; &gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html">   47</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1IncompleteCholesky.html">IncompleteCholesky</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SparseSolverBase.html">SparseSolverBase</a>&lt;IncompleteCholesky&lt;Scalar,UpLo_,OrderingType_&gt; &gt;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;{</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseSolverBase.html">SparseSolverBase&lt;IncompleteCholesky&lt;Scalar,UpLo_,OrderingType_&gt;</a> &gt; <a class="code" href="classEigen_1_1SparseSolverBase.html">Base</a>;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> RealScalar;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keyword">typedef</span> OrderingType_ OrderingType;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> OrderingType::PermutationType PermutationType;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> PermutationType::StorageIndex StorageIndex;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix&lt;Scalar,ColMajor,StorageIndex&gt;</a> <a class="code" href="classEigen_1_1SparseMatrix.html">FactorType</a>;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">VectorSx</a>;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;RealScalar,Dynamic,1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">VectorRx</a>;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;StorageIndex,Dynamic, 1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">VectorIx</a>;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keyword">typedef</span> std::vector&lt;std::list&lt;StorageIndex&gt; &gt; VectorList;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keyword">enum</span> { UpLo = UpLo_ };</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      ColsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>,</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;      MaxColsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    };</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a85eaef081ac008cfb2d9fe2c761906f1">   75</a></span>&#160;    <a class="code" href="classEigen_1_1IncompleteCholesky.html#a85eaef081ac008cfb2d9fe2c761906f1">IncompleteCholesky</a>() : m_initialShift(1e-3),m_analysisIsOk(false),m_factorizationIsOk(false) {}</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a164f124d27dcc86066eee7abc25f234f">   80</a></span>&#160;    <a class="code" href="classEigen_1_1IncompleteCholesky.html#a164f124d27dcc86066eee7abc25f234f">IncompleteCholesky</a>(<span class="keyword">const</span> MatrixType&amp; matrix) : m_initialShift(1e-3),m_analysisIsOk(false),m_factorizationIsOk(false)</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    {</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;      <a class="code" href="classEigen_1_1IncompleteCholesky.html#ac967d9c0f6fca7fc70ead69cc9c6bd83">compute</a>(matrix);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    }</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a52df89ac8dba637444a2246574b70593">   86</a></span>&#160;    EIGEN_CONSTEXPR <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1IncompleteCholesky.html#a52df89ac8dba637444a2246574b70593">rows</a>() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_L.<a class="code" href="classEigen_1_1SparseMatrix.html#a853a76dd42349fa2f3654a4a61e0f574">rows</a>(); }</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
<div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#ad036ff94ea84db68f5c2b6350a885073">   89</a></span>&#160;    EIGEN_CONSTEXPR <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1IncompleteCholesky.html#ad036ff94ea84db68f5c2b6350a885073">cols</a>() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_L.<a class="code" href="classEigen_1_1SparseMatrix.html#a36b8cc95234b4e2de38a199b6b2af9fc">cols</a>(); }</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a11a53c3787990c0287f7296f72779509">  100</a></span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1IncompleteCholesky.html#a11a53c3787990c0287f7296f72779509">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;IncompleteCholesky is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;      <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    }</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#afe6b11310e22c1853577746a37fbcdc7">  108</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteCholesky.html#afe6b11310e22c1853577746a37fbcdc7">setInitialShift</a>(RealScalar shift) { m_initialShift = shift; }</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#ad822e66656638a9cf84087ed228514e7">  113</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteCholesky.html#ad822e66656638a9cf84087ed228514e7">analyzePattern</a>(<span class="keyword">const</span> MatrixType&amp; mat)</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    {</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;      OrderingType ord;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      PermutationType pinv;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;      ord(mat.template selfadjointView&lt;UpLo&gt;(), pinv);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;      <span class="keywordflow">if</span>(pinv.size()&gt;0) m_perm = pinv.inverse();</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;      <span class="keywordflow">else</span>              m_perm.resize(0);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;      m_L.<a class="code" href="classEigen_1_1SparseMatrix.html#a835ae5b304ddbb187eac25d5850b2ced">resize</a>(mat.rows(), mat.cols());</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;      m_analysisIsOk = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;      m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160; </div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00134"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a715fd8371885458f6317a7d63353b8d5">  134</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteCholesky.html#a715fd8371885458f6317a7d63353b8d5">factorize</a>(<span class="keyword">const</span> MatrixType&amp; mat);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#ac967d9c0f6fca7fc70ead69cc9c6bd83">  143</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteCholesky.html#ac967d9c0f6fca7fc70ead69cc9c6bd83">compute</a>(<span class="keyword">const</span> MatrixType&amp; mat)</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    {</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;      <a class="code" href="classEigen_1_1IncompleteCholesky.html#ad822e66656638a9cf84087ed228514e7">analyzePattern</a>(mat);</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;      <a class="code" href="classEigen_1_1IncompleteCholesky.html#a715fd8371885458f6317a7d63353b8d5">factorize</a>(mat);</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    }</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="comment">// internal</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest&gt;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> Rhs&amp; b, Dest&amp; x)<span class="keyword"> const</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;      eigen_assert(m_factorizationIsOk &amp;&amp; <span class="stringliteral">&quot;factorize() should be called first&quot;</span>);</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;      <span class="keywordflow">if</span> (m_perm.rows() == b.rows())  x = m_perm * b;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;      <span class="keywordflow">else</span>                            x = b;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;      x = m_scale.asDiagonal() * x;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;      x = m_L.template triangularView&lt;Lower&gt;().solve(x);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;      x = m_L.adjoint().template triangularView&lt;Upper&gt;().solve(x);</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;      x = m_scale.asDiagonal() * x;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;      <span class="keywordflow">if</span> (m_perm.rows() == b.rows())</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        x = m_perm.inverse() * x;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#ad7b709e4f100630cfd6d8ed90f75aa40">  165</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1SparseMatrix.html">FactorType</a>&amp; <a class="code" href="classEigen_1_1IncompleteCholesky.html#ad7b709e4f100630cfd6d8ed90f75aa40">matrixL</a>()<span class="keyword"> const </span>{ eigen_assert(m_factorizationIsOk &amp;&amp; <span class="stringliteral">&quot;factorize() should be called first&quot;</span>); <span class="keywordflow">return</span> m_L; }</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160; </div>
<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a79251fafbc557fa3bef58024b7e9c939">  168</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">VectorRx</a>&amp; <a class="code" href="classEigen_1_1IncompleteCholesky.html#a79251fafbc557fa3bef58024b7e9c939">scalingS</a>()<span class="keyword"> const </span>{ eigen_assert(m_factorizationIsOk &amp;&amp; <span class="stringliteral">&quot;factorize() should be called first&quot;</span>); <span class="keywordflow">return</span> m_scale; }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160; </div>
<div class="line"><a name="l00171"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteCholesky.html#a8681a4ea582d778eb712a10bb809b1ed">  171</a></span>&#160;    <span class="keyword">const</span> PermutationType&amp; <a class="code" href="classEigen_1_1IncompleteCholesky.html#a8681a4ea582d778eb712a10bb809b1ed">permutationP</a>()<span class="keyword"> const </span>{ eigen_assert(m_analysisIsOk &amp;&amp; <span class="stringliteral">&quot;analyzePattern() should be called first&quot;</span>); <span class="keywordflow">return</span> m_perm; }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    FactorType m_L;              <span class="comment">// The lower part stored in CSC</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    VectorRx m_scale;            <span class="comment">// The vector for scaling the matrix</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    RealScalar m_initialShift;   <span class="comment">// The initial shift parameter</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <span class="keywordtype">bool</span> m_analysisIsOk;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keywordtype">bool</span> m_factorizationIsOk;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    PermutationType m_perm;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160; </div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> updateList(<a class="code" href="classEigen_1_1Ref.html">Ref&lt;const VectorIx&gt;</a> colPtr, <a class="code" href="classEigen_1_1Ref.html">Ref&lt;VectorIx&gt;</a> rowIdx, <a class="code" href="classEigen_1_1Ref.html">Ref&lt;VectorSx&gt;</a> vals, <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&amp; col, <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&amp; jk, VectorIx&amp; firstElt, VectorList&amp; listCol);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;};</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="comment">// Based on the following paper:</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="comment">//   C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="comment">//   Limited memory, SIAM J. Sci. Comput.  21(1), pp. 24-45, 1999</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="comment">//   http://ftp.mcs.anl.gov/pub/tech_reports/reports/P682.pdf</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> UpLo_, <span class="keyword">typename</span> OrderingType&gt;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteCholesky.html#a715fd8371885458f6317a7d63353b8d5">IncompleteCholesky&lt;Scalar,UpLo_, OrderingType&gt;::factorize</a>(<span class="keyword">const</span> MatrixType_&amp; mat)</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;{</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  eigen_assert(m_analysisIsOk &amp;&amp; <span class="stringliteral">&quot;analyzePattern() should be called first&quot;</span>);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160; </div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  <span class="comment">// Dropping strategy : Keep only the p largest elements per column, where p is the number of elements in the column of the original matrix. Other strategies will be added</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="comment">// Apply the fill-reducing permutation computed in analyzePattern()</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  <span class="keywordflow">if</span> (m_perm.rows() == mat.rows() ) <span class="comment">// To detect the null permutation</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  {</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    <span class="comment">// The temporary is needed to make sure that the diagonal entry is properly sorted</span></div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    FactorType tmp(mat.rows(), mat.cols());</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    tmp = mat.template selfadjointView&lt;UpLo_&gt;().twistedBy(m_perm);</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    m_L.template selfadjointView&lt;Lower&gt;() = tmp.template selfadjointView&lt;Lower&gt;();</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  {</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    m_L.template selfadjointView&lt;Lower&gt;() = mat.template selfadjointView&lt;UpLo_&gt;();</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  }</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160; </div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = m_L.cols();</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nnz = m_L.nonZeros();</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  Map&lt;VectorSx&gt; vals(m_L.valuePtr(), nnz);         <span class="comment">//values</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  Map&lt;VectorIx&gt; rowIdx(m_L.innerIndexPtr(), nnz);  <span class="comment">//Row indices</span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  Map&lt;VectorIx&gt; colPtr( m_L.outerIndexPtr(), n+1); <span class="comment">// Pointer to the beginning of each row</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  VectorIx firstElt(n-1); <span class="comment">// for each j, points to the next entry in vals that will be used in the factorization</span></div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  VectorList listCol(n);  <span class="comment">// listCol(j) is a linked list of columns to update column j</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  VectorSx col_vals(n);   <span class="comment">// Store a  nonzero values in each column</span></div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  VectorIx col_irow(n);   <span class="comment">// Row indices of nonzero elements in each column</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  VectorIx col_pattern(n);</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  col_pattern.fill(-1);</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  StorageIndex col_nnz;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  <span class="comment">// Computes the scaling factors</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  m_scale.resize(n);</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  m_scale.setZero();</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; n; j++)</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = colPtr[j]; k &lt; colPtr[j+1]; k++)</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    {</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;      m_scale(j) += numext::abs2(vals(k));</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;      <span class="keywordflow">if</span>(rowIdx[k]!=j)</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;        m_scale(rowIdx[k]) += numext::abs2(vals(k));</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    }</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  m_scale = m_scale.cwiseSqrt().cwiseSqrt();</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    <span class="keywordflow">if</span>(m_scale(j)&gt;(std::numeric_limits&lt;RealScalar&gt;::min)())</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;      m_scale(j) = RealScalar(1)/m_scale(j);</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;      m_scale(j) = 1;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="comment">// TODO disable scaling if not needed, i.e., if it is roughly uniform? (this will make solve() faster)</span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  <span class="comment">// Scale and compute the shift for the matrix</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  RealScalar mindiag = NumTraits&lt;RealScalar&gt;::highest();</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; n; j++)</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  {</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = colPtr[j]; k &lt; colPtr[j+1]; k++)</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      vals[k] *= (m_scale(j)*m_scale(rowIdx[k]));</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    eigen_internal_assert(rowIdx[colPtr[j]]==j &amp;&amp; <span class="stringliteral">&quot;IncompleteCholesky: only the lower triangular part must be stored&quot;</span>);</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    mindiag = numext::mini(numext::real(vals[colPtr[j]]), mindiag);</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  }</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  FactorType L_save = m_L;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  RealScalar shift = 0;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  <span class="keywordflow">if</span>(mindiag &lt;= RealScalar(0.))</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    shift = m_initialShift - mindiag;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160; </div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">NumericalIssue</a>;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160; </div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  <span class="comment">// Try to perform the incomplete factorization using the current shift</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  <span class="keywordtype">int</span> iter = 0;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <span class="keywordflow">do</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  {</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="comment">// Apply the shift to the diagonal elements of the matrix</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; n; j++)</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;      vals[colPtr[j]] += shift;</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="comment">// jki version of the Cholesky factorization</span></div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j=0;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    <span class="keywordflow">for</span> (; j &lt; n; ++j)</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    {</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;      <span class="comment">// Left-looking factorization of the j-th column</span></div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;      <span class="comment">// First, load the j-th column into col_vals</span></div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;      Scalar diag = vals[colPtr[j]];  <span class="comment">// It is assumed that only the lower part is stored</span></div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;      col_nnz = 0;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = colPtr[j] + 1; i &lt; colPtr[j+1]; i++)</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;      {</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;        StorageIndex l = rowIdx[i];</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;        col_vals(col_nnz) = vals[i];</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        col_irow(col_nnz) = l;</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;        col_pattern(l) = col_nnz;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;        col_nnz++;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;      }</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;      {</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        <span class="keyword">typename</span> std::list&lt;StorageIndex&gt;::iterator k;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        <span class="comment">// Browse all previous columns that will update column j</span></div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;        <span class="keywordflow">for</span>(k = listCol[j].begin(); k != listCol[j].end(); k++)</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        {</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;          <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> jk = firstElt(*k); <span class="comment">// First element to use in the column</span></div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;          eigen_internal_assert(rowIdx[jk]==j);</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;          Scalar v_j_jk = numext::conj(vals[jk]);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160; </div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;          jk += 1;</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;          <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = jk; i &lt; colPtr[*k+1]; i++)</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;          {</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;            StorageIndex l = rowIdx[i];</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;            <span class="keywordflow">if</span>(col_pattern[l]&lt;0)</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;            {</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;              col_vals(col_nnz) = vals[i] * v_j_jk;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;              col_irow[col_nnz] = l;</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;              col_pattern(l) = col_nnz;</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;              col_nnz++;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;            }</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;              col_vals(col_pattern[l]) -= vals[i] * v_j_jk;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;          }</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;          updateList(colPtr,rowIdx,vals, *k, jk, firstElt, listCol);</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;        }</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;      }</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160; </div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;      <span class="comment">// Scale the current column</span></div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;      <span class="keywordflow">if</span>(numext::real(diag) &lt;= 0)</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;      {</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;        <span class="keywordflow">if</span>(++iter&gt;=10)</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;          <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160; </div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;        <span class="comment">// increase shift</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;        shift = numext::maxi(m_initialShift,RealScalar(2)*shift);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;        <span class="comment">// restore m_L, col_pattern, and listCol</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;        vals = Map&lt;const VectorSx&gt;(L_save.valuePtr(), nnz);</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;        rowIdx = Map&lt;const VectorIx&gt;(L_save.innerIndexPtr(), nnz);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;        colPtr = Map&lt;const VectorIx&gt;(L_save.outerIndexPtr(), n+1);</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;        col_pattern.fill(-1);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;        <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=0; i&lt;n; ++i)</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;          listCol[i].clear();</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160; </div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;        <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;      }</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160; </div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;      RealScalar rdiag = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(numext::real(diag));</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;      vals[colPtr[j]] = rdiag;</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k&lt;col_nnz; ++k)</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      {</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = col_irow[k];</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;        <span class="comment">//Scale</span></div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;        col_vals(k) /= rdiag;</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        <span class="comment">//Update the remaining diagonals with col_vals</span></div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;        vals[colPtr[i]] -= numext::abs2(col_vals(k));</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;      }</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;      <span class="comment">// Select the largest p elements</span></div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      <span class="comment">// p is the original number of elements in the column (without the diagonal)</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = colPtr[j+1] - colPtr[j] - 1 ;</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      Ref&lt;VectorSx&gt; cvals = col_vals.head(col_nnz);</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;      Ref&lt;VectorIx&gt; cirow = col_irow.head(col_nnz);</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;      internal::QuickSplit(cvals,cirow, p);</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;      <span class="comment">// Insert the largest p elements in the matrix</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cpt = 0;</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = colPtr[j]+1; i &lt; colPtr[j+1]; i++)</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;      {</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;        vals[i] = col_vals(cpt);</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;        rowIdx[i] = col_irow(cpt);</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;        <span class="comment">// restore col_pattern:</span></div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        col_pattern(col_irow(cpt)) = -1;</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;        cpt++;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;      }</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;      <span class="comment">// Get the first smallest row index and put it after the diagonal element</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> jk = colPtr(j)+1;</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;      updateList(colPtr,rowIdx,vals,j,jk,firstElt,listCol);</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    }</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160; </div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <span class="keywordflow">if</span>(j==n)</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;    {</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;      m_factorizationIsOk = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;      m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;    }</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  } <span class="keywordflow">while</span>(m_info!=<a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>);</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;}</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160; </div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> UpLo_, <span class="keyword">typename</span> OrderingType&gt;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> IncompleteCholesky&lt;Scalar,UpLo_, OrderingType&gt;::updateList(Ref&lt;const VectorIx&gt; colPtr, Ref&lt;VectorIx&gt; rowIdx, Ref&lt;VectorSx&gt; vals, <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&amp; col, <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&amp; jk, VectorIx&amp; firstElt, VectorList&amp; listCol)</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;{</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  <span class="keywordflow">if</span> (jk &lt; colPtr(col+1) )</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  {</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = colPtr(col+1) - jk;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> minpos;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    rowIdx.segment(jk,p).minCoeff(&amp;minpos);</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    minpos += jk;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    <span class="keywordflow">if</span> (rowIdx(minpos) != rowIdx(jk))</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    {</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;      <span class="comment">//Swap</span></div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;      std::swap(rowIdx(jk),rowIdx(minpos));</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;      std::swap(vals(jk),vals(minpos));</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    }</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    firstElt(col) = internal::convert_index&lt;StorageIndex,Index&gt;(jk);</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    listCol[rowIdx(jk)].push_back(internal::convert_index&lt;StorageIndex,Index&gt;(col));</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  }</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;}</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160; </div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160; </div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;<span class="preprocessor">#endif</span></div>
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<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_a11a53c3787990c0287f7296f72779509"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#a11a53c3787990c0287f7296f72779509">Eigen::IncompleteCholesky::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdoc">Reports whether previous computation was successful.</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:100</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_a164f124d27dcc86066eee7abc25f234f"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#a164f124d27dcc86066eee7abc25f234f">Eigen::IncompleteCholesky::IncompleteCholesky</a></div><div class="ttdeci">IncompleteCholesky(const MatrixType &amp;matrix)</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:80</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_a52df89ac8dba637444a2246574b70593"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#a52df89ac8dba637444a2246574b70593">Eigen::IncompleteCholesky::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:86</div></div>
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<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_a79251fafbc557fa3bef58024b7e9c939"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#a79251fafbc557fa3bef58024b7e9c939">Eigen::IncompleteCholesky::scalingS</a></div><div class="ttdeci">const VectorRx &amp; scalingS() const</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:168</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_a85eaef081ac008cfb2d9fe2c761906f1"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#a85eaef081ac008cfb2d9fe2c761906f1">Eigen::IncompleteCholesky::IncompleteCholesky</a></div><div class="ttdeci">IncompleteCholesky()</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:75</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_a8681a4ea582d778eb712a10bb809b1ed"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#a8681a4ea582d778eb712a10bb809b1ed">Eigen::IncompleteCholesky::permutationP</a></div><div class="ttdeci">const PermutationType &amp; permutationP() const</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:171</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_ac967d9c0f6fca7fc70ead69cc9c6bd83"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#ac967d9c0f6fca7fc70ead69cc9c6bd83">Eigen::IncompleteCholesky::compute</a></div><div class="ttdeci">void compute(const MatrixType &amp;mat)</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:143</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_ad036ff94ea84db68f5c2b6350a885073"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#ad036ff94ea84db68f5c2b6350a885073">Eigen::IncompleteCholesky::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:89</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_ad7b709e4f100630cfd6d8ed90f75aa40"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#ad7b709e4f100630cfd6d8ed90f75aa40">Eigen::IncompleteCholesky::matrixL</a></div><div class="ttdeci">const FactorType &amp; matrixL() const</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:165</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_ad822e66656638a9cf84087ed228514e7"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#ad822e66656638a9cf84087ed228514e7">Eigen::IncompleteCholesky::analyzePattern</a></div><div class="ttdeci">void analyzePattern(const MatrixType &amp;mat)</div><div class="ttdoc">Computes the fill reducing permutation vector using the sparsity pattern of mat.</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:113</div></div>
<div class="ttc" id="aclassEigen_1_1IncompleteCholesky_html_afe6b11310e22c1853577746a37fbcdc7"><div class="ttname"><a href="classEigen_1_1IncompleteCholesky.html#afe6b11310e22c1853577746a37fbcdc7">Eigen::IncompleteCholesky::setInitialShift</a></div><div class="ttdeci">void setInitialShift(RealScalar shift)</div><div class="ttdoc">Set the initial shift parameter .</div><div class="ttdef"><b>Definition:</b> IncompleteCholesky.h:108</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix&lt; Scalar, Dynamic, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1Ref_html"><div class="ttname"><a href="classEigen_1_1Ref.html">Eigen::Ref</a></div><div class="ttdoc">A matrix or vector expression mapping an existing expression.</div><div class="ttdef"><b>Definition:</b> Ref.h:285</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html">Eigen::SparseMatrix&lt; Scalar, ColMajor, StorageIndex &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html_a36b8cc95234b4e2de38a199b6b2af9fc"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a36b8cc95234b4e2de38a199b6b2af9fc">Eigen::SparseMatrix::cols</a></div><div class="ttdeci">Index cols() const</div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:142</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html_a835ae5b304ddbb187eac25d5850b2ced"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a835ae5b304ddbb187eac25d5850b2ced">Eigen::SparseMatrix::resize</a></div><div class="ttdeci">void resize(Index rows, Index cols)</div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:626</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html_a853a76dd42349fa2f3654a4a61e0f574"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a853a76dd42349fa2f3654a4a61e0f574">Eigen::SparseMatrix::rows</a></div><div class="ttdeci">Index rows() const</div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:140</div></div>
<div class="ttc" id="aclassEigen_1_1SparseSolverBase_html"><div class="ttname"><a href="classEigen_1_1SparseSolverBase.html">Eigen::SparseSolverBase</a></div><div class="ttdoc">A base class for sparse solvers.</div><div class="ttdef"><b>Definition:</b> SparseSolverBase.h:70</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">Eigen::NumericalIssue</a></div><div class="ttdeci">@ NumericalIssue</div><div class="ttdef"><b>Definition:</b> Constants.h:446</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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